PHIL 120 - Therefore as he picks up a particular dish and...

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Bayes’ Theorem Practice Mickey and Ann have a friend that cleans compulsively and well. Needless to say, they invite him to dinner whenever the dishes start piling up. On one such occasion, over their “strenuous” protests, they acquiesce to his wishes, allowing him to do the dishes. What they don’t know is that he actually does this not out of compulsive cleaning habits, but out of compulsive Bayesianism. Using the relative theory of probability, the friend has ascertained the following: Mickey pre-rinses often, and so a pre-rinsed dish is 90% likely to be his, while the pre- rinsed dish belongs to Ann only 10% of the time.
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Unformatted text preview: Therefore, as he picks up a particular dish and notices that it is not pre-rinsed, 1 he immediately infers that it is Ann’s. However, as he begins the cleaning process, he notices that the leftover food falls into the category which Mickey refers to as “pointless comestibles” (that is, food that involves neither meat nor sugar). He knows that, while Ann eats pointless comestibles in 70% of her meals, Mickey does so with only 15% of his meals. Consider: 1) Has his belief as to whose dish it was changed? 2) With what certainty does he now hold his belief? 1 It is not his dish, as he pre-rinses 100% of the time....
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